Here is the full list of all 10 Kero Blaster trophies - there are 5 bronze, 4 silver and 1 gold.
Beat Normal Mode
Beat the game without getting wiped out
Beat the game with 2 lives remaining
Beat the game while wearing the jacket
Complete Zangyou Mode
Beat Zangyou Mode without getting wiped out
Beat Zangyou Mode with 2 lives remaining
Beat Zangyou Mode while wearing the jacket
Complete Omake Mode
Beat Omake Mode while wearing the jacket